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Computable isomorphism

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In computability theory two sets of natural numbers are computably isomorphic or recursively isomorphic if there exists a total computable and bijective function such that the image of restricted to equals , i.e. .

Further, two numberings and are called computably isomorphic if there exists a computable bijection so that . Computably isomorphic numberings induce the same notion of computability on a set.

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Theorems

By the Myhill isomorphism theorem, the relation of computable isomorphism coincides with the relation of mutual one-one reducibility.[1]

References

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